Least Common Multiple of 223 and 224

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 223 and 224 the smallest integer that is 49952 that is divisible by both numbers.

Least Common Multiple (LCM) of 223 and 224 is 49952.

LCM(223,224) = 49952

LCM of 223 and 224

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 223 and 224

LCM of 223 and 224 is 49952

Least common multiple can be found by multiplying the highest exponent prime factors of 223 and 224. First we will calculate the prime factors of 223 and 224.

Prime Factorization of 223


223 223
1

Prime factors of 223 are 223. Prime factorization of 223 in exponential form is:

223 = 2231

Prime Factorization of 224


2 224
2 112
2 56
2 28
2 14
7 7
1

Prime factors of 224 are 2,7. Prime factorization of 224 in exponential form is:

224 = 25×71

Now multiplying the highest exponent prime factors to calculate the LCM of 223 and 224.

LCM(223,224) = 25×71×2231
LCM(223,224) = 49952

Factors of 223

List of positive integer factors of 223 that divides 223 without a remainder.

1, 223

Factors of 224

List of positive integer factors of 224 that divides 224 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

Least Common Multiple of 223 and 224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 223 and 224, than apply into the LCM equation.

GCF(223,224) = 1
LCM(223,224) = ( 223 × 224) / 1
LCM(223,224) = 49952 / 1
LCM(223,224) = 49952

Properties of LCM 223 and 224

(i) The LCM of 224 and 223 is associative

LCM of 223 and 224 = LCM of 224 and 223

Related Least Common Multiples of 223

Related Least Common Multiples of 224

Frequently Asked Questions on LCM of 223 and 224

1. What is the LCM of 223 and 224?

Answer: LCM of 223 and 224 is 49952.

2. What are the Factors of 223?

Answer: Factors of 223 are 1, 223. There are 2 integers that are factors of 223. The greatest factor of 223 is 223.

3. What are the Factors of 224?

Answer: Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. There are 12 integers that are factors of 224. The greatest factor of 224 is 224.

4. How to Find the LCM of 223 and 224?

Answer:

Least Common Multiple of 223 and 224 = 49952

Step 1: Find the prime factorization of 223

223 = 223

Step 2: Find the prime factorization of 224

224 = 2 x 2 x 2 x 2 x 2 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 49952 = 2 x 2 x 2 x 2 x 2 x 7 x 223

Step 4: Therefore, the least common multiple of 223 and 224 is 49952.